# LIB2-026 — A rank-character action represents the selector Hessian

- class: CLAIM · review_state: PUBLISHED · house_tier: not yet assigned
- labels as printed: math_status Certified · attachment NOT_PRINTED · scorecard tier word none (PDF p.296)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The registered rank-normalized carrier-character action Fchar has a critical point at the base with ∇²Fchar(I) = QT, and its displayed coefficients are traced to carrier ranks.

## Caution

A variational representation of QT does not supply a microscopic principle selecting Fchar or its nonlinear shape.

## Primary source

Appendix S, §9.1, Theorem 9.1: critical point and Hessian, PDF p.313: "has its critical point at the base with ∇2 Fchar (I) = QT exactly"

## Machine

- url: /library-v2/LIB2-026/
- content_sha256: d4dd4615a4746e327c4f299e50cebf956c386c6804e44bd3d92a636fa5579360
- candidate_ids: C2-107

## Freshness

- BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02
- Declared volatile fields (R36): BUILD_STAMP